Abstract

We present recent studies on cellular automata (CAs) viewed as discrete dynamical systems. In the first part, we illustrate the relations between two important notions: subshift attractors and signal subshifts, measure attractors and particle weight functions. The second part of the chapter considers some operations on the space of one-dimensional CA configurations, namely, shifting and lifting, showing that they conserve many dynamical properties while reducing complexity. The final part reports recent investigations on two-dimensional CA. In particular, we report a construction (slicing construction) that allows us to see a two-dimensional CA as a one-dimensional one and to lift some one-dimensional results to the two-dimensional case.